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Chapter 1: Linear and Quadratic functions By Chris Muffi Vocabulary◦ ◦ ◦ ◦ ◦ Coordinates- ordered pair of numbers x-axis- is the horizontal line y-axis- is the vertical line Origin- the x and y- axis point of origin Quadrants- the axis divides them into 4 of them ◦ Solution- is an ordered pair of numbers that makes the equation true. 1-1 Points and Lines 1-1 Formulas to know Mid-Point Formula: M x1 x 2 y1 y 2 = 2 , 2 Distance Formula Ab= x2 x1 2 y2 y1 2 1-1 Example Use A(4, 2), B(2, 10), C(-2, 9), and D(0, 1). A. Show that AC and BD bisect each other. B. Show that AC = BC. C. What kind of figure is ABCD? D. Find the length of AC . E. Find the midpoint of AC . 1-2 Slope of lines Slope m rise y 2 y1 run x2 x1 Facts to know ◦ Horizontal lines have a slope of zero ◦ Vertical lines have no slope ◦ Negative slopes fall to the right y= mx + b is slope intercept form Slope-intercept form 1-3 Equations of Lines Formulas: ◦ General Form Ax + By= C ◦ Slope intercept Form y = mx + B ◦ Point Slope Form y y1 m x x1 ◦ Intercept Form x y 1 a b Function- describes a dependent relationship between two quantities Linear functions have the form f(x) = mx +B 1-4 Linear Functions and Models Domain- is the set of values for which the function is defined. You can think of the domain of a function as the set of input values. Domain The set of output values is called the range of the function. Range 1-5 Complex Numbers Counting Numbers are 1, 2, 3.. Rational Numbers are ratios of integers, to represent fractional parts of quantities. Irrational Numbers are like these 2 Complex These numbers are commonly referred to as imaginary numbers. And look like these 1 and 15 i 1 i 1 1 1 2 i 1 1 1 i 3 i 1 1 1 1 1 4 i 1 1 1 1 1 i 5 i 1ofImaginary 1 1 1 1 1 1 Pattern 6 1-6 Solving Quadratic Equations quadratic equation- equation that can be written in the form ax 2 bx c 0 where a≠0 Roots ◦ A root, or solution, of a quadratic equation is a value of the variable that satisfies the equation. completing the square- method of transforming a quadratic equation so that one side is a perfect square trinomial Steps: ◦ Step 1: Divide both sides by the coefficient of so that will have a coefficient of 1. ◦ Step 2: Subtract the constant term from both sides. ◦ Step 3: Complete the square. Add the square of one half the coefficient of x to both sides. ◦ Step 4: Take the square root of both sides and solve for x. Completing the Square Quadratic Formula quadratic formula- derived by completing the square. b b 2 4ac x 2a 1-7 Quadratic Functions a ≠ 0, is the set of points (x, y) that satisfies the equation y ax 2 bx c then this graph is a parabola X and Y- Intercept The y-intercept of a parabola with equation y ax 2 bx c is c. If b 2 4ac > 0, there are two xintercepts. 2 If b 4ac = 0, there is one x-intercept (at a point where the parabola and the x-axis are tangent to each other). 2 If b 4ac < 0, there are no xintercepts.